Adaptive mixed integer nonlinear programming for process management

ABSTRACT

Real-time dynamic process modeling in an online model-based process control computing environment. A solver system utilizes an oracle to implement adaptive algorithms for a mixed integer nonlinear programming (MINLP) solver and a nonlinear programming (NLP) solver.

BACKGROUND

Conventional tools for continuous process optimization employcalculations designed to determine optimal operating states ofcontinuous processes, such as refinery, chemical, or petrochemical plantoperations. When an optimal decision requires the switching on orswitching off of units, conventional systems and methods for continuousoptimization utilize a Mixed Integer Nonlinear Programming (MINLP)solver and unit models that simulate the switching behavior of thedesired process units. The MINLP solvers implemented by conventionalsystems and methods look for optimal solutions in all possible regions,which is complex and time-consuming. Moreover, conventional systems andmethods that utilize computing devices to implement MINLP solvers arenot optimized to efficiently use the processors and/or memory of thecomputing devices.

SimSci ROMeo, available from Schneider Electric, is a Rigorous On-lineModeling and Equation-based Optimization (ROMEO) module for continuousprocess optimization.

SUMMARY

Aspects of the present invention improve the fields of process controland automation and process simulation by employing onlinefirst-principles simulation techniques in conjunction with a MixedInteger Nonlinear Programming (MINLP) solver in real-time. An oraclethat comprises a solver system provides adaptive algorithms that manageinfeasible solutions and enhance robustness of solutions. Aspects of theinvention allow the determination of an optimal operating state whileavoiding searching computationally expensive infeasible paths,generating feasible paths automatically, generating groupingsautomatically to reduce infeasible space, and/or reducing the searchspace based on initial feasibility. Aspects of the present inventionalso provide improvements in computer technology, namely, process modelsimulation and optimization.

In an aspect, a system includes one or more sensors and a controlsystem. The sensors provide data representing a current state of each ofa plurality of process units within a continuous process. The processunits meet one or more demands of the continuous process. The controlsystem receives the current state data and generates an operating stateof the continuous process based on the data. The control system includesa processor executing computer-executable components. The componentsinclude a plurality of model components, a plurality of switchcomponents, a MINLP solver component, and an oracle component. The modelcomponents implement at least one first-principle equation thatrepresents at least one of the process units. One or more of the modelcomponents comprise a group. The switch components each comprise acorresponding one of the model components and each implement a MINLPbehavior of the corresponding model component. The MINLP solvercomponent is configured to specify a switching state from a plurality ofswitching states. The switching states each correspond to an operationalstatus of the plurality of model components. The oracle component isconfigured to provide an infeasibility indication to the MINLP solvercomponent as a function of the demands for indicating whether thespecified switching state is infeasible.

In another aspect, a computer-implemented method generates an optimaloperating state of a continuous process. The method includes a controlsystem receiving data from at least one sensor within the continuousprocess. The data represents a current state of each of a plurality ofprocess units within the continuous process. The process units meet oneor more demands of the continuous process. The method also includes thecontrol system simulating an operation of a plurality of unit models inconjunction with a MINLP solver in real-time. The unit models eachrepresent one of the plurality of process units via at least onefirst-principle equation. The unit models each have a MINLP switchimplementing MINLP behavior of the unit model. Each MINLP switch encodesat least one operating constraint of the continuous process. Moreover,the method includes the control system generating an infeasibilityindication as a function of the demands. The infeasibility indicationindicates whether a switching state of a plurality of switching statesis feasible. The switching states each correspond to an operationalstatus of the unit models.

In yet another aspect, a computer-readable storage device storescomputer-executable modules that, when executed by a processor, generatean operating state of a continuous process. The modules include aplurality of model modules, a plurality of MINLP switch modules, and asolver module. The model modules each define a plurality of unit modelsthat represent a process unit within the continuous process via at leastone first-principle equation during an execution of the model module bythe processor. The process unit meets at least one demand of thecontinuous process. The MINLP switch modules each transition acorresponding model module between an active state and an inactivestate. The transitioning is based at least in part on a parameterencoding at least one operating constraint of the continuous processduring an execution of the MINLP switch module by the processor. TheMINLP switch modules each implement an MINLP behavior of thecorresponding model module. The solver module simulates an operation ofeach of the model modules and the MINLP switch modules in real-timeduring an execution of the solver module by the processor. Thesimulation generates the operating state of the continuous process basedon a state of the plurality of MINLP switch modules when the solvermodule determines the state of the plurality of MINLP switch modules isfeasible as a function of the demand.

Other objects and features will be in part apparent and in part pointedout hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an exemplary ROMEO solver system embodyingaspects of the invention.

FIG. 2 is a block diagram of an exemplary continuous process embodyingaspects of the invention.

FIG. 3 is a flow chart illustrating an exemplary workflow process ofconsidering only feasible spaces embodying aspects of the invention.

FIG. 4 is an illustration of an exemplary decision tree representingpossible solutions in accordance with aspects of the invention.

FIGS. 5 and 6 are flow charts illustrating exemplary workflow processesof automatically generating feasible paths embodying aspects of theinvention.

FIG. 7 is a flow chart illustrating an exemplary workflow process ofautomatically generating groupings in accordance with aspects of theinvention.

FIGS. 8 and 9 are flow charts illustrating exemplary workflow processesof reducing a search space based on initial feasibility in accordancewith aspects of the invention.

Corresponding reference characters indicate corresponding partsthroughout the drawings.

DETAILED DESCRIPTION

Referring now to the drawings, FIG. 1 is a block diagram of a ROMEOsolver system embodying aspects of the invention, including implementingMixed Integer Nonlinear Programming (MINLP) behavior. In one form,computer-executable instructions are executed to solve a process problemby an MINLP switch in conjunction with constraints of a model that cansimulate the behavior of desired process units. The illustrated systemincludes a modeling system 102, a model-variable module 104, aconstraint module 106, an MINLP switch 108, a process 110, a sensor 112,process input data 114, a process definition interface 116, a solversystem 118, a MINLP solver module 120, a feasibility evaluator oracle122, a NLP solver 124, and an optimal operating state 126. In anembodiment, FIG. 1 illustrates an MINLP modeling system and method.Non-invasive MINLP modeling systems and methods, as described in U.S.patent application Ser. No. 14/745,961, filed Jun. 6, 2015, and herebyincorporated by reference in its entirety, may also be utilized withaspects of the present invention.

Systems and methods described herein solve nonlinear process problemswhile optimizing for certain considerations (e.g., operating penalty,cost, etc.) while ensuring the process meets plant constraints. Aspectsof the present invention are described herein with respect to optimizingenergy source usage in a continuous process but it is to be understoodby one skilled in the art that the systems and methods described hereinare also capable of optimizing continuous processes with respect toconsiderations other than energy source usage.

Energy source (e.g., utility) optimization in continuous processesinvolves calculating the best solution to meet the energy demand, whileoperating the underlying process optimally with desired operationalspecifications and keeping the operational expenses as low as possible.In order to perform a quantum of work in a process, there is a need forsome amount of energy. The utility optimization problem is relevant whenthere are multiple energy sources that can supply the desired quantum ofenergy. For example, there may be some sources of energy endemic to theprocess and other sources of energy that are extraneous to the process.Utility optimization requires the capability to switch among availableenergy sources depending on the economics, energy and material balance,and underlying nonlinear process optimality. These computational issuesrequire an MINLP solver in conjunction with models that can simulate theswitching behavior of process units. While modeling the process forMINLP, it is advantageous to encode operational constraints of theprocess or plant into the model. Such constraints simplify the task forthe MINLP solver by focusing the search for a solution in only thefeasible regions. Grouping of units that comprise a process model as amechanism to implement constraints for MINLP utility optimization, asdescribed in U.S. patent application Ser. No. 14/977,785, filed Dec. 22,2015, and hereby incorporated by reference in its entirety, may also beutilized with aspects of the present invention.

The utility optimization problem solved by aspects of the presentinvention can be expressed in general mathematical form. Consider anonlinear process modeled with equality constraints f(x,y,z)=0, wherethe function f is nonlinear in the vector variables x, y, and z. Let f:R^(N)×R^(S)×B^(B)→R^(N), illustrating the dimension of these quantities,where typically, S<N. The variables of vector x are free-dependent andcan be varied between some operational bounds of the process (e.g., ofdimension N×1). The variables of vector y are free-independent variablesand usually referred to as a “specification” and also varied betweenbounds of the process (e.g., of dimension S×1). In an embodiment, S<N.The variables of vector z are free-independent and z is the vector ofinteger switches in the problem. In an embodiment, variables in vector zvary between [0, 1] and is of dimension B×1. Given a cost functionc(x,y,z), the utility optimization problem, assuming minimization ofcost, is:min_(xyz)c(x,y,z)  (Equation 1)subject tof(x,y,z)=0andx_(min)≤x≤X_(max), y_(min)≤y≤y_(max), and z∈B^(B)A Rigorous Online Modeling and Equation-based Optimization (ROMEO)modeling system, as described herein, allows a user to construct aflowsheet of the process with models or units from a pre-built libraryor from models built by the user. These models encode the quantities f,c, x, and y in Equation 1. The ROMEO modeling system also includes plantoperation constraints that specify some special structure to binaryvariable switching. Aspects of the present invention described hereinencompass the incorporation of a feasibility evaluator oracle thatprovides an indication (e.g., a “yes/no” answer) of whether a switchingis feasible. For example, such indication allows aspects of the presentinvention to prune out further switching below an infeasible switching,which increases the efficiency (e.g., percent of nodes visited forsolution), performance (e.g., time to solution), and robustness (e.g.,fewer failing nodes) of the ROMEO modeling system.

Referring further to FIG. 1, in an embodiment, the unit model module 102(i.e., unit) comprises a storage memory device having stored thereonprocessor-executable instructions for defining a first-principle modelof a unit comprising a continuous process that has been modified toimplement MINLP behavior. In an exemplary embodiment, unit 102 defines afirst-principle model of a motor in the process 110 and includes themodel-variable module 104, the constraint module 106, and the MINLPswitch 108. Additional units include, but are not limited to,generators, steam turbines, boiler fuel flows, motors, shafts, and thelike. Additional details of unit 102 are further described herein and inU.S. patent application Ser. Nos. 14/745,961 and 14/977,785, eachincorporated by reference above.

Still referring to FIG. 1, the model-variable module 104 comprises, inan embodiment, a storage memory device having stored thereonprocess-executable instructions for defining a model-variable of thefirst-principle model of unit 102. In an exemplary embodiment,model-variable module 104 defines the shaft power of a motor as themodel-variable of interest. Other model-variables include, but are notlimited to, the shaft power of a generator, the actual work of a steamturbine, and flow rate of boiler fuel flows. Additional details ofmodel-variable module 104 are further described herein and in U.S.patent application Ser. Nos. 14/745,961 and 14/977,785, eachincorporated by reference above.

In one embodiment of the present invention, the constraint module 106comprises a storage memory device having stored thereonprocessor-executable instructions for defining one or more constraintsof the first-principle model of unit 102. In an exemplary embodiment,constraint module 106 defines a minimum value (e.g., 0) and a maximumvalue (e.g., 100) of the shaft power of a motor.

In a further embodiment, operation of a continuous process, such asthose employed at industrial plants, involves several constraints basedon factors such as capacity, safety, economics, and the like. Forexample, due to bus-bar current loading limits, there might be aconstraint that either one of two motors connected to the same bus-barscan operate at a time. Similarly, constraints may exist regardingswitching in either a motor or a steam turbine to meet a given load, butnot both simultaneously. Additionally, there may be constraints thatspecify a group of units should operate simultaneously if required bythe load demands and the units by themselves cannot meet the demand. Inan exemplary general case, there may be a need to encode more complexoperational constraints. Aspects of the present invention as furtherdescribed herein provide solutions to these situations by specifying andencoding operational constraints (e.g., of a plant) through automaticgrouping of model units. In an embodiment, grouping is a specificationof a set of units that should be constrained to behave in a certainmanner, as further described herein and U.S. patent application Ser. No.14/977,785, incorporated by reference above.

The MINLP switch 108 of FIG. 1 comprises a storage memory device havingstored thereon processor-executable instructions for implementing MINLPbehavior in the first-principle model of unit 102, in an exemplaryembodiment. For example, MINLP switch 108 may implement MINLP behaviorin a motor model defined by unit 102 by modifying the shaft power of themotor. In an embodiment, a unit 102 including MINLP switch 108 isreferred to as an MINLP unit 102. Additional details of MINLP switch 108are further described herein and in U.S. patent application Ser. Nos.14/745,961 and 14/977,785, each incorporated by reference above. Inaccordance with aspects of the invention, MINLP switch 108 may bereferred to as a switch component in some embodiments.

According to embodiments of the invention, process 110 is a continuousprocess, such as a refinery, chemical, or petrochemical plant operation,for example, and/or its control system. In an embodiment, process 110includes at least one sensor 112. Other aspects of process 110 arefurther defined herein. The process definition interface 116 receivesprocess input data 114 from a source such as a user, another softwareprogram, or a device (e.g., a sensor and/or a unit in process 110), forexample. The process input data 114 represents a current state ofprocess 110 and corresponds to the process problem to be solved. Theprocess definition interface 116 provides the received process inputdata 114 to the solver system 118 for use in executing an interactivemodel to solve the process problem as described herein. In an exemplaryembodiment, process definition interface 116 is part of a ROMEO modelingsystem that allows a user to construct a flowsheet of process 110 withmodels or units from a pre-built library or from models built by theuser.

The solver system 118 comprises a storage memory device having storedthereon processor-executable instructions for defining an iterativeprocess having variables. The variables have certain values which, whenapplied to the iterative process, converge the iterative process to asolution. The variables have other values, which, when applied to theiterative process, do not converge the iterative process to a solution.In one form, solver system 118 comprises a ROMEO module. In theembodiment illustrated by FIG. 1, solver system 118 includes an MINLPsolver module 120 and a NLP solver module 124. The MINLP solver module120 solves MINLP problems and the NLP solver module 124 solves nonlinearprogramming (NLP) problems in accordance with an embodiment of theinvention. The solver system 118 is adapted for changing the value of abinary MINLP variable in order to switch unit 102 on and off in thesimulation while converging to an optimal solution (e.g., optimaloperating state 126) for the underlying nonlinear process 118. In anembodiment, solver system 118, including aspects thereof, generates anoperating state (e.g., optimal operating state 126) based on a previousoperating state of a process (e.g., process 118) when the state of MINLPswitch 108 is infeasible. Commonly assigned U.S. patent application Ser.No. 13/968,119, which describes a nonlinear correction factor module foruse with, for example, a ROMEO solver, is incorporated by reference inits entirety. Additional details regarding solver system 118 are furtherdescribed in U.S. patent application Ser. Nos. 14/745,961 and14/977,785, each incorporated by reference above.

The feasibility evaluator oracle 122 of FIG. 1 comprises a storagememory device having stored thereon processor-executable instructionsfor providing an indication of whether a switching state of one or moreunits 102 is feasible. The oracle 122 examines one or more demands onthe system to determine feasibility. For example, oracle 122 determineswhether a power-balance on a shaft can be met without actually computingthe power-balance in accordance with aspects of the invention. In anembodiment, oracle 122 is intended to execute before NLP solver 124executes to solve a given node of MINLP switching. For example, when anexecution of oracle 122 determines that a given node is feasible, oracle122 returns an affirmative indication (e.g., “yes”) to NLP solver 124which will then execute to evaluate the cost of that switching. But whenan execution of oracle 122 determines that a given node is infeasible,oracle 122 returns a negative indication (e.g., “no”) to MINLP solver120 thereby pruning out any further switching below the current node andNLP solver 124 will not evaluate that node. In an embodiment, oracle 122assumes that the demand at unit 102 (e.g., at shafts or at sinks) isfixed. In another embodiment, demand at unit 102 is variable andbracketed between a known upper limit and a known lower limit. In suchan embodiment, oracle 122 utilizes either the upper limit (e.g., maximumfor non-generator MINLP devices) and/or the lower limit (e.g., minimumfor generator MINLP devices) to provide a conservative indication ofswitching infeasibility. In accordance with aspects of the presentinvention, oracle 122 utilizes the minimum and maximum of the load ofeach unit 102 used for switching, the status of the MINLP switch 108 foreach unit 102 (e.g., ON, OFF, continuous), the load at each shaft thathas a MILNP device attached, and the minimum and maximum of sourcessupplying a stream when a MINLP device is attached to such stream andthe load at the sinks. Additional details of oracle 122 are providedherein.

In an exemplary embodiment, at least unit model module 102 and solversystem 118 comprise a control system adapted for transmitting controlinformation to components (e.g., actuators) within process 110 andreceiving sensory and feedback data from components (e.g., sensor 112)within process 110. For example, the control system and process 110 maycommunicate via a telecommunications network that facilitates theexchange of data, such as those that operate according to the IEEE 802.3(e.g., Ethernet) and/or the IEEE 802.11 (e.g., Wi-Fi) protocols, forexample. In another embodiment, the control system and process 110communicate via any medium that allows data to be physically transferredthrough serial or parallel communication channels (e.g., copper wire,optical fiber, computer bus, wireless communication channel, etc.). Inadditional exemplary embodiments, the control system is one of adistributed control system (DCS) and a centralized database run in anonline mode.

FIG. 2 illustrates an exemplary process 110 including a steam source202, a turbine 204, a motor 206, a generator 208, a shaft 210, and adriven process 212. In this exemplary embodiment, turbine 204, motor206, and generator 208 are attached to shaft 210 that requires 20 unitsof work. Also in this embodiment, turbine 204 can supply 30 units ofwork at a cost of 300, motor 206 can supply 20 units of work at a costof 200, and generator 208 can consume 10 units of work at a cost of −50.NLP-feasibility requires the work around shaft 210 to be balanced. Table1 illustrates the possible states for turbine 204, motor 206, andgenerator 208 for the embodiment of FIG. 2.

TABLE 1 NLP Feasibility State Motor Turbine Generator Cost Contribution(Difference) Remarks A 0 0 0 0 0 No (−20) B 0 0 1 −50 −10 No (−30) C 0 10 300 30 No (10) D 0 1 1 250 20 Yes Sub-optimal E 1 0 0 200 20 YesOptimal F 1 0 1 150 10 No (−10) G 1 1 0 500 50 No (−30) H 1 1 1 450 40No (−20)In an embodiment, each state of Table 1 is a node in a decision tree.Table 1 shows that when turbine 204 and generator 208 are on and motor206 is off (i.e., State D) the state is feasible with a cost of 250.Table 1 also shows that when motor 206 is on and turbine 204 andgenerator 208 are both off (i.e., State E) the state is also feasiblebut with a reduced cost of 200. Thus, both State D and State E arefeasible solutions, but State E is the optimal solution. Table 1 alsoshows that States A-C and F-H are infeasible and thus calculating thepower-balance for those states results in needless complexity, time, andusage of computing resources. Aspects of the present invention preventuseless NLP evaluations.

By grouping turbine 204, motor 206, and generator 208 in accordance withU.S. patent application Ser. No. 14/977,785, infeasible switching may beprevented in accordance with aspects of the invention. For example,putting turbine 204, motor 206, and generator 208 into a single groupwith motor 206 marked as complement would have avoided infeasible StatesA-C and F-H. Table 2 illustrates the three independent binary variables(e.g., turbine 204, motor 206, generator 208) collapsed to just oneindependent group leader binary variable with motor 206 serving as thegroup leader.

TABLE 2 Motor (Group Contri- NLP Leader) Turbine Generator Cost butionFeasibility Remarks 0 1 1 250 20 Yes Sub-optimal 1 0 0 200 20 YesOptimalWhen grouping is scaled up to a large number of devices, it may becomeincreasingly difficult for a user to cover all feasible switching statesusing grouping alone, which may lead to infeasible branches for MINLPwith potential robustness issues and wasted computation time. Aspects oforacle 122 alleviate these concerns by providing an indication ofwhether a switching state is feasible without actually computing thepower-balance.

The following provides a generic mathematical description for oracle 122and further details of oracle 122 are provided herein. In an embodiment,the load to be serviced at a given shaft is represented as L. Equation 2represents a power-balance at the shaft, assuming all MINLP devicesconnected to the shaft are known.F=Σ _(i=1) ^(N) ^(devices) D _(i) P _(i) −L  (Equation 2)When F=0 then the solution is feasible and when F is non-zero then thesolution is infeasible. Device switch D_(i) is either 0 or 1 based oneach device's switching state, which has a relation to its group leaderbased on its complement. Power P_(i) is the power contributed by thedevice, which is positive for a motor or a turbine, but negative for agenerator. In an embodiment in which the switch is considered as acontinuum for a node, D_(i)=1 for Equation 2. There may existembodiments that are more complex than situations Equation 2 can handle.For example, when units that do not have MINLP capability are connectedto a shaft, Equation 2 must be partitioned appropriately for units thatare fixed and those that can be switched. Moreover, switchable devicesmay be varied over a range of loads, between a minimum and a maximum,and otherwise supply no power. In such embodiments, feasibility becomesa containment problem (i.e., given a range, determine whether the loadcan be met). The oracle 122 handles such embodiments by determiningwhether the power-balance can be met using the provided ranges (i.e., isfeasible or infeasible) without actually computing the power-balance.

FIG. 3 illustrates a sample workflow process 300 in a ROMEO-based solversystem for determining feasibility. In an embodiment, the process 300comprises a three-stage computation at a shaft (e.g., shaft 210). Atstep 302, MINLP solver module 120 specifies a next switching state whena solution is incomplete. The oracle 122 is initialized at step 304. Inan embodiment, initialization is a one-time occurrence. In anotherembodiment, initialization includes obtaining data representing theminimum and maximum range of loads for a device, a status of the device,and/or a current load on the device. The oracle 122 determines thefeasibility of non-MINLP devices at step 306. In an embodiment, oracle122 computes Equation 3 during step 306.F ₁=Σ_(k=1) ^(N) ^(non-MINLP devices) P _(k) −L  (Equation 3)where F₁ is the feasibility of the non-MINLP devices, P_(k) is the powercontributed by the k-th device and L is the load to be serviced at theshaft. At step 308, oracle 122 determines whether F₁ is infeasible. WhenF₁ is greater than zero, the solution is infeasible. Either L shouldincrease by a shift in the process equilibrium or the problem isinfeasible. When the solution is infeasible, process 300 continues backto step 302. When F₁ is less than or equal to zero in Equation 3, oracle122 does not detect infeasibility and process 300 continues to step 310.

At step 310, oracle 122 determines the feasibility of MINLP devices. Inan embodiment, oracle 122 computes Equation 4 during step 310.F ₂ =F ₁+Σ_(i=1) ^(N) ^(MINLP devices) D _(i) P _(i) ^(MAX)  (Equation4)where D_(i) is the device switch for the i-th device and P_(i) ^(MAX) isthe maximum load of the i-th device. At a given node of MINLP, all ofthe device switch variables D_(i) are known, and are either 0 or 1(continuum switches have D=1). In an embodiment, Equation 4 does notcontain any generators. The oracle 122 determines whether infeasibilityis detected via Equation 4 at step 312. When F₂ is negative the solutionis infeasible and process 300 returns to step 302. When F₂ isnon-negative the solution is feasible and process 300 continues to step314.

At step 314, oracle 122 determines the feasibility of MINLP generatorson the shaft turned on (e.g., D=1). In an embodiment, oracle 122computes Equation 5 during step 314.F ₃ =F ₂−Σ_(i=1) ^(N) ^(MINLP generators) D _(i) P _(i)^(MIN)  (Equation 5)where D_(i) is the device switch for the i-th generator and P_(i) ^(MIN)is the minimum load of the i-th generator. The negative sign in front ofthe summation is necessary because the generators increase the load. Atstep 316, oracle 122 determines whether infeasibility is detected byEquation 5. When F₃ is negative, it implies an imbalance at the shaftand therefore the switching is infeasible. In this case, process 300returns to step 302 without calculating any other shaft. When F₃ ispositive or zero, the switching is feasible. When all shafts return suchfeasibility, process 300 continues to step 318 where NLP solver 124computes the NLP solution at that node.

Referring further to FIG. 3, oracle 122 provides a conservativedetermination of infeasibility because such determination results in apruning of that branch and a false determination degrades performance.One having ordinary skill in the art will understand that if oracle 122makes a determination of feasibility but is wrong, NLP solver module 124will still catch the infeasibility, albeit at a greater cost. In anembodiment, a feasibility heuristic according to process 300 isapplicable to cases in which the horsepower of the loads at shafts arefixed and/or variable within known limits. In another embodiment,process 300 is applicable in cases of stream switching in which thesinks have fixed flows or flows within known limits. In yet anotherembodiment, aspects of oracle 122 that perform process 300 arecontrolled using a parameter of MINLP solver module 120. Aspects oforacle 122 thus improve the efficiency, performance, and robustness ofsolver system 118.

FIG. 4 illustrates an exemplary decision tree 400 in accordance withaspects of the invention. In an embodiment, decision tree 400corresponds to Equation 5 in which each node corresponds to a NLPproblem (e.g., restriction) and each edge corresponds to a branchingdecision (e.g., steps 308, 312, 316 in process 300). As shown, oracle122 obtains feasibility data at node 402 and performs a depth-firstsearch by selecting branch 404-A. Selecting branch 404-A leads to node406. In an exemplary embodiment, process 300 is performed by solversystem 118 at node 406. The oracle 122 executing according to theembodiment of process 300 determines that the node that would resultfrom selecting branch 408-A is infeasible and thus the nodes that wouldfollow from that node are also infeasible. Accordingly, branch 408-A ispruned (e.g., fathomed) such that the nodes resulting from that branchare never solved thereby resulting in reduced time finding a feasiblesolution. In the operation of process 300, pruning a branch correspondsto detecting infeasibility at steps 308, 312, and/or 316 and returningto step 302.

Referring again to FIG. 4, selecting branch 408-B leads to node 410where oracle 122 determines that selecting branch 412-B has a highercost than the initial cost, as further described herein. The oracle 122thus selects branch 412-A which leads to node 414. The node that wouldresult from selecting branch 416-A is infeasible and thus that branch ispruned. The oracle 122 selects branch 416-B to reach node 418. Theoracle again determines that selecting branch 420-A would result in aninfeasible node so it selects branch 420-B. The branch 420-B leads to asolution at node 422 that is feasible but non-optimal.

The oracle 122 returns to node 402 to select branch 404-B which leads tonode 424. At node 424, oracle 122 determines that branch 426-A wouldresult in an infeasible solution. The oracle 122 selects branch 426-Bwhich leads to node 428. Selecting branch 430-B leads to node 432, butboth branches at node 432 are infeasible so oracle 122 thus selectsbranch 430-A which leads to node 434. The oracle 122 determines thatselecting branch 436-A would lead to an infeasible solution so itselects branch 436-B which leads to node 438. At node 438, oracle 122determines that selecting branch 440-A leads to another infeasiblesolution. The oracle 122 thus selects branch 440-B which leads to asolution at node 442 that is feasible and is the optimal solution.

FIG. 5 illustrates another sample workflow process 500 in a ROMEO-basedsolver system for automatic generation of a feasible path by oracle 122.In an embodiment, the number of switchable devices in a continuousprocess (e.g., process 110) may not change over time due to largecapital costs, for example. In this embodiment, the loading and cost ofenergy will change more frequently than the number of switchabledevices. They types of switching may vary greatly and include loading,energy costs, start-up costs, and shutdown costs. In such processes withstable operations, results determined by MILNP solver module 120 willtend to resemble past solutions and MINLP solver module 120 is expectedto find similar infeasible paths each time it executes. In such cases,performance of a solver system can be enhanced by keeping track ofinfeasible paths and avoiding those paths in future executions.

In an embodiment, aspects of the invention utilize logical constraintsto avoid infeasible paths during an execution. The oracle 122 in thisembodiment is a heuristic that utilizes a memory of infeasible paths atthe solver level and performs NLP only for switching states that arepermitted by not being on the list. The process 500 proceeds fromprevious feasibility evaluations and NLP evaluations at step 502 to adetermination by oracle 122 of whether the current solution is feasibleat step 504. As an example, consider State F in Table 1 in which turbine204 being off and both motor 206 and generator 208 being on results inan infeasible solution. In this embodiment, oracle 122 seeks toinvalidate this switching state in future executions when Equation 6 istrue.MTG=0  (Equation 6)where T=(1−T). In the embodiment, oracle 122 adds Equation 6 as anautomatically generated logical cut to a list of such cuts that isremembered at the solver-level (e.g., solver system 118) rather than themodel-level (e.g., unit 102) at step 506. A list of cuts is preferablystored on a storage memory device. In accordance with aspects of theinvention, the list-based automatic generation of feasible paths byoracle 122 operates at the group level rather than on individualdevices. The constraint in Equation 6 reduces to the feasible space asshown in Table 3.

TABLE 3 Motor Turbine Generator M(1-T)G Feasibility 0 0 0 0 Yes 0 0 1 0Yes 0 1 0 0 Yes 0 1 1 0 Yes 1 0 0 0 Yes 1 0 1 1 No 1 1 0 0 Yes 1 1 1 0YesAfter step 506, process 508 proceeds to step 508 in which MINLP solvermodule 120 specifies the next switching state if the solution isincomplete. When the solution is not infeasible (i.e., the solution isfeasible) process 500 continues directly to step 508. In an embodiment,aspects of oracle 122 that perform process 500 are controlled using aparameter of MINLP solver module 120. Aspects of oracle 122 thus improvethe efficiency, performance, and robustness of solver system 118.

FIG. 6 illustrates a sample workflow process 600 in a ROMEO-based solversystem for utilization of a list of infeasible switching states byoracle 122. At step 602, MINLP solver module 120 issues a new node forNLP evaluation if the solution is incomplete. At step 604, oracle 122checks this node against the list of cuts to determine whether theswitching is infeasible. For example, if the new node includes aswitching that is included in the stored list, then the switching isinfeasible and process 600 returns to step 602. If the new node includesa switching that is not included in the stored list, then the switchingis not infeasible and process 600 proceeds to other feasibilityevaluations and NLP evaluations at step 606. In an embodiment, aspectsof oracle 122 that perform process 600 are controlled using a parameterof MINLP solver module 120. Aspects of oracle 122 thus improve theefficiency, performance, and robustness of solver system 118.

FIG. 7 illustrates a sample workflow process 700 in a ROMEO-based solversystem for automatic generation of groups of units 102 by oracle 122. Inaccordance with aspects of the invention, oracle 122 automaticallygenerates groups of units 102 to alleviate challenges of manuallycreating groups when the number of switchable devices increases. In anembodiment, a user may specify one or more groups involving a few units102 while leaving the rest of the devices in their own default groups inaccordance with U.S. patent application Ser. No. 14/977,785,incorporated above by reference. Aspects of the present invention groupthe remaining units 102 in such a manner that feasible solutions are notexcluded. In an embodiment, when the first feasible solution is found(e.g., all binary variables equal to zero or one) oracle 122 puts allungrouped binary variables in a single group, including complements asnecessary to represent the first feasible solution. As the solutionprocess proceeds, additional feasible solutions are utilized by oracle122 to refine the group by partitioning it into two groups. In otherwords, oracle 122 moves the set members that face contraction at the newsolution to a new group in which there is no contradiction betweenmembers. The process of partitioning continues with each feasiblesolution found. In the worst case, there will be as many partitions asthe default groups. In the best case, there will be just one new group.

As an example, consider the decision tree 400 illustrated by FIG. 4. Inthis example, each left side branch (e.g., those having an “-A” suffix)is a logical “0” and each right side branch (e.g., those having a “-B”suffix) is a logical “1”. When oracle 122 reaches the non-optimal butfeasible solution at node 422, oracle 122 creates a group of binaryvariables to represent that solution. The group for node 422 isrepresented by Group (a):{−x1,x2,−x3,x4,x5}  (a)wherein a negative sign correlates to a complement in the group. Whenoracle 122 reaches the optimal solution at node 442, oracle 122 createsanother group of binary variables to represent the solution (e.g.,according to process 700 described herein). The group for node 442 isrepresented by temporary Group (b):{x1,x2,−x3,x4,x5}  (b)When comparing the two groups, oracle 122 determines that there is acontradiction for the x1 variable but the other variables satisfy bothgroups. The oracle 122 then partitions Group (a) into two sets (e.g.,groups) represented by Group (c):{x1} and {x2,−x3,x4,x5}  (c)The oracle 122 uses these partitions in Group (c) which has twoconsistent groups for the discovered feasible solutions. If additionalsolutions result in further contradictions, oracle 122 proceeds topartition the groups accordingly.

Referring further to FIG. 7, process 700 begins with oracle 122initializing at step 702. At step 704, oracle 122 determines whether thesolution is binary feasible. When oracle 122 determines the solution isnot binary feasible, process 700 continues to step 710 in which MINLPsolver module 120 specifies the next switching state if the solution isincomplete. When oracle 122 determines the solution is binary feasible,process 700 continues to step 706. Referring to the above example,oracle 122 would determine binary feasibility at nodes 422 and 442 (FIG.4). At step 706, oracle 122 determines whether the current solutioncontradicts an existing group. When oracle 122 determines the solutiondoes not contradict any existing groups, process 700 continues to step710. When oracle 122 determines the solution does contradict an existinggroup, process 700 continues to step 708. Referring to the aboveexample, oracle 122 would determine the solution represented by Group(b) contradicts the solution represented by Group (a). At step 708,oracle 122 creates new groups for contradicting members before advancingto step 710. Referring again to the above example, oracle 122 wouldcreate Group (c) at step 708.

In an embodiment, oracle 122 executing in accordance with the embodimentof process 700 permits the automatic generation of grouping constraintsby studying the history of solutions. In another embodiment, oracle 122learns from valid solutions. In yet another embodiment, aspects oforacle 122 that perform process 700 are controlled using a parameter ofMINLP solver module 120 that will disable such behavior ifuser-requested.

FIG. 8 illustrates yet another sample workflow process 800 in aROMEO-based solver system for using an initial feasibility cost. Inaccordance with aspects of the invention, the initial state of acontinuous process (e.g., process 110) is in either an ON state or anOFF state. The initial state is a feasible solution for the MINLPproblem because the process is already in that state. It could be inthis state, for example, as a consequence of an MINLP optimizationperformed during a previous cycle. Aspects of the present inventioncomplete a MINLP optimization in less time than conventional solutionsby pruning nodes that have higher costs than the initial solution. AMINLP solution is started at step 802. At step 804, oracle 122 computesthe cost at the initial state. In an embodiment, oracle 122 assumes thatthe constraints are closed (e.g., the process is at a valid solution)and all integer variables are at integer values. At step 806, oracle 122determines whether the initial value is solved and is binary feasible.When oracle 122 determines that either the initial value is not solvedor is not binary feasible at step 806, process 800 continues to step 810in which MINLP solver module 120 commences execution. When oracle 122determines that the initial value is solved and is binary feasible atstep 806, process 800 continues to step 808. At step 808, oracle 122stores the initial cost computed in step 804 as a threshold value beforecontinuing to step 810. In an embodiment, the initial cost is stored asa threshold on a memory storage device.

FIG. 9 illustrates a sample workflow process 900 in a ROMEO-based solversystem for using an initial feasibility cost to prune branches with ahigher cost than the initial cost. At step 902, MINLP solver module 120issues a new node for NLP evaluation if the solution is incomplete.Oracle 122 then performs feasibility evaluations at step 904. NLP solvermodule 124 performs an NLP evaluation of the specified switching at step906. At step 908, oracle 122 determines whether the state has beensolved and the cost is greater than the threshold. When either the statehas not been solved or the cost is less than the threshold, process 900returns back to step 902. When the state has been solved and the cost isgreater than the threshold, process 900 continues to step 910. At step910, oracle 122 alerts MINLP solver module 120 to prune the branchbefore returning back to step 902.

Referring again to FIG. 4, decision tree 400 illustrates aspects ofsteps 908 and 910 of process 900. For example, oracle 122 executingaccording to process 900 at node 410 may determine that branch 412-B hasa higher cost than the threshold cost at step 908. The oracle 122 alertsMINLP solver module 120 to prune branch 412-B and MINLP solver module120 specifies the next switching (e.g., branch 412-A).

In an embodiment, process 900 utilizes the cost computed in process 800as a “best so far” cost which is used to prune higher cost nodes. Inthis manner, the search is restricted to only those nodes that havepotential as lower cost nodes which improves the efficiency andperformance of the MINLP solution.

Embodiments of the present invention may comprise a special purposecomputer including a variety of computer hardware, as described ingreater detail below.

Embodiments within the scope of the present invention also includecomputer-readable media for carrying or having computer-executableinstructions or data structures stored thereon. Such computer-readablemedia can be any available media that can be accessed by a specialpurpose computer. By way of example, and not limitation, suchcomputer-readable media can comprise RAM, ROM, EEPROM, CD-ROM or otheroptical disk storage, magnetic disk storage, or other magnetic storagedevices, or any other medium that can be used to carry or store desiredprogram code means in the form of computer-executable instructions ordata structures and that can be accessed by a general purpose or specialpurpose computer. When information is transferred or provided over anetwork or another communications connection (either hardwired,wireless, or a combination of hardwired or wireless) to a computer, thecomputer properly views the connection as a computer-readable medium.Thus, any such connection is properly termed a computer-readable medium.Combinations of the above should also be included within the scope ofcomputer-readable media. Computer-executable instructions comprise, forexample, instructions and data which cause a general purpose computer,special purpose computer, or special purpose processing device toperform a certain function or group of functions.

The following discussion is intended to provide a brief, generaldescription of a suitable computing environment in which aspects of theinvention may be implemented. Although not required, aspects of theinvention will be described in the general context ofcomputer-executable instructions, such as program modules, beingexecuted by computers in network environments. Generally, programmodules include routines, programs, objects, components, datastructures, etc. that perform particular tasks or implement particularabstract data types. Computer-executable instructions, associated datastructures, and program modules represent examples of the program codemeans for executing steps of the methods disclosed herein. Theparticular sequence of such executable instructions or associated datastructures represent examples of corresponding acts for implementing thefunctions described in such steps.

Those skilled in the art will appreciate that aspects of the inventionmay be practiced in network computing environments with many types ofcomputer system configurations, including personal computers, hand-helddevices, multi-processor systems, microprocessor-based or programmableconsumer electronics, network PCs, minicomputers, mainframe computers,and the like. Aspects of the invention may also be practiced indistributed computing environments where tasks are performed by localand remote processing devices that are linked (either by hardwiredlinks, wireless links, or by a combination of hardwired or wirelesslinks) through a communications network. In a distributed computingenvironment, program modules may be located in both local and remotememory storage devices.

An exemplary system for implementing aspects of the invention includes aspecial purpose computing device in the form of a conventional computer,including a processing unit, a system memory, and a system bus thatcouples various system components including the system memory to theprocessing unit. The system bus may be any of several types of busstructures including a memory bus or memory controller, a peripheralbus, and a local bus using any of a variety of bus architectures. Thesystem memory includes read only memory (ROM) and random access memory(RAM). A basic input/output system (BIOS), containing the basic routinesthat help transfer information between elements within the computer,such as during start-up, may be stored in ROM. Further, the computer mayinclude any device (e.g., computer, laptop, tablet, PDA, cell phone,mobile phone, a smart television, and the like) that is capable ofreceiving or transmitting an IP address wirelessly to or from theinternet.

The computer may also include a magnetic hard disk drive for readingfrom and writing to a magnetic hard disk, a magnetic disk drive forreading from or writing to a removable magnetic disk, and an opticaldisk drive for reading from or writing to removable optical disk such asa CD-ROM or other optical media. The magnetic hard disk drive, magneticdisk drive, and optical disk drive are connected to the system bus by ahard disk drive interface, a magnetic disk drive-interface, and anoptical drive interface, respectively. The drives and their associatedcomputer-readable media provide nonvolatile storage ofcomputer-executable instructions, data structures, program modules, andother data for the computer. Although the exemplary environmentdescribed herein employs a magnetic hard disk, a removable magneticdisk, and a removable optical disk, other types of computer readablemedia for storing data can be used, including magnetic cassettes, flashmemory cards, digital video disks, Bernoulli cartridges, RAMs, ROMs,solid state drives (SSDs), and the like.

The computer typically includes a variety of computer readable media.Computer readable media can be any available media that can be accessedby the computer and includes both volatile and nonvolatile media,removable and non-removable media. By way of example, and notlimitation, computer readable media may comprise computer storage mediaand communication media. Computer storage media include both volatileand nonvolatile, removable and non-removable media implemented in anymethod or technology for storage of information such as computerreadable instructions, data structures, program modules or other data.Computer storage media are non-transitory and include, but are notlimited to, RAM, ROM, EEPROM, flash memory or other memory technology,CD-ROM, digital versatile disks (DVD) or other optical disk storage,SSDs, magnetic cassettes, magnetic tape, magnetic disk storage or othermagnetic storage devices, or any other medium which can be used to storethe desired non-transitory information, which can accessed by thecomputer. Alternatively, communication media typically embody computerreadable instructions, data structures, program modules or other data ina modulated data signal such as a carrier wave or other transportmechanism and includes any information delivery media.

Program code means comprising one or more program modules may be storedon the hard disk, magnetic disk, optical disk, ROM, and/or RAM,including an operating system, one or more application programs, otherprogram modules, and program data. A user may enter commands andinformation into the computer through a keyboard, pointing device, orother input device, such as a microphone, joy stick, game pad, satellitedish, scanner, or the like. These and other input devices are oftenconnected to the processing unit through a serial port interface coupledto the system bus. Alternatively, the input devices may be connected byother interfaces, such as a parallel port, a game port, or a universalserial bus (USB). A monitor or another display device is also connectedto the system bus via an interface, such as video adapter 48. Inaddition to the monitor, personal computers typically include otherperipheral output devices (not shown), such as speakers and printers.

One or more aspects of the invention may be embodied incomputer-executable instructions (i.e., software), routines, orfunctions stored in system memory or nonvolatile memory as applicationprograms, program modules, and/or program data. The software mayalternatively be stored remotely, such as on a remote computer withremote application programs. Generally, program modules includeroutines, programs, objects, components, data structures, etc. thatperform particular tasks or implement particular abstract data typeswhen executed by a processor in a computer or other device. The computerexecutable instructions may be stored on one or more tangible,non-transitory computer readable media (e.g., hard disk, optical disk,removable storage media, solid state memory, RAM, etc.) and executed byone or more processors or other devices. As will be appreciated by oneof skill in the art, the functionality of the program modules may becombined or distributed as desired in various embodiments. In addition,the functionality may be embodied in whole or in part in firmware orhardware equivalents such as integrated circuits, application specificintegrated circuits, field programmable gate arrays (FPGA), and thelike.

The computer may operate in a networked environment using logicalconnections to one or more remote computers. The remote computers mayeach be another personal computer, a tablet, a PDA, a server, a router,a network PC, a peer device, or other common network node, and typicallyinclude many or all of the elements described above relative to thecomputer. The logical connections include a local area network (LAN) anda wide area network (WAN) that are presented here by way of example andnot limitation. Such networking environments are commonplace inoffice-wide or enterprise-wide computer networks, intranets and theInternet.

When used in a LAN networking environment, the computer is connected tothe local network through a network interface or adapter. When used in aWAN networking environment, the computer may include a modem, a wirelesslink, or other means for establishing communications over the wide areanetwork, such as the Internet. The modem, which may be internal orexternal, is connected to the system bus via the serial port interface.In a networked environment, program modules depicted relative to thecomputer, or portions thereof, may be stored in the remote memorystorage device. It will be appreciated that the network connectionsshown are exemplary and other means of establishing communications overwide area network may be used.

Preferably, computer-executable instructions are stored in a memory,such as the hard disk drive, and executed by the computer.Advantageously, the computer processor has the capability to perform alloperations (e.g., execute computer-executable instructions) inreal-time.

The order of execution or performance of the operations in embodimentsof the invention illustrated and described herein is not essential,unless otherwise specified. That is, the operations may be performed inany order, unless otherwise specified, and embodiments of the inventionmay include additional or fewer operations than those disclosed herein.For example, it is contemplated that executing or performing aparticular operation before, contemporaneously with, or after anotheroperation is within the scope of aspects of the invention.

Embodiments of the invention may be implemented with computer-executableinstructions. The computer-executable instructions may be organized intoone or more computer-executable components or modules. Aspects of theinvention may be implemented with any number and organization of suchcomponents or modules. For example, aspects of the invention are notlimited to the specific computer-executable instructions or the specificcomponents or modules illustrated in the figures and described herein.Other embodiments of the invention may include differentcomputer-executable instructions or components having more or lessfunctionality than illustrated and described herein.

When introducing elements of aspects of the invention or the embodimentsthereof, the articles “a”, “an”, “the” and “said” are intended to meanthat there are one or more of the elements. The terms “comprising”,“including”, and “having” are intended to be inclusive and mean thatthere may be additional elements other than the listed elements.

Having described aspects of the invention in detail, it will be apparentthat modifications and variations are possible without departing fromthe scope of aspects of the invention as defined in the appended claims.As various changes could be made in the above constructions, products,and methods without departing from the scope of aspects of theinvention, it is intended that all matter contained in the abovedescription and shown in the accompanying drawings shall be interpretedas illustrative and not in a limiting sense.

What is claimed is:
 1. A system, comprising: one or more sensorsproviding data representing a current state of each of a plurality ofprocess units within a continuous process, said process units meetingone or more demands of the continuous process; and a control systemreceiving the current state data and generating an operating state ofthe continuous process based thereon, the control system comprising: amodel circuit implementing at least one first-principle equation,wherein the at least one first-principle equation represents at leastone of the process units; a switch circuit corresponding to the modelcircuit and implementing a mixed integer nonlinear programming (MINLP)behavior of the corresponding model circuit; a MINLP solver circuitconfigured to specify a switching state from a plurality of switchingstates, the switching states each corresponding to an operational statusof the model circuit; and an oracle circuit configured to provide aninfeasibility indication to the MINLP solver circuit as a function ofthe demands for indicating whether the specified switching state isinfeasible.
 2. The system of claim 1, further comprising a nonlinearprogramming (NLP) solver circuit configured to generate the operatingstate of the continuous process, wherein the operating state isoptimized in accordance with one or more constraints of the continuousprocess in response to receiving an indication from the oracle circuitthat the specified switching state is feasible.
 3. The system of claim1, wherein the oracle circuit is further configured to: compute anon-MINLP feasibility of one or more non-MINLP process units of theplurality of process units; compute a MINLP non-generator feasibility ofone or more MINLP non-generator process units of the plurality ofprocess units and the non-MINLP feasibility; and compute a MINLPgenerator feasibility of one or more MINLP generator process units ofthe plurality of process units and the MINLP non-generator feasibility,wherein the infeasibility indication is based on the non-MINLPfeasibility, the MINLP non-generator feasibility, and the MINLPgenerator feasibility.
 4. The system of claim 3, wherein the oraclecircuit is further configured to provide an infeasible indication whenthe non-MINLP feasibility is greater than zero, wherein the oraclecircuit is further configured to provide the infeasible indication whenthe MINLP non-generator feasibility is less than zero, and wherein theoracle circuit is further configured to provide the infeasibleindication when the MINLP generator feasibility is one of zero andgreater than zero.
 5. The system of claim 3, wherein the plurality ofprocess units within the continuous process include a shaft, and whereina demand at the shaft is fixed.
 6. The system of claim 3, wherein theplurality of process units within the continuous process include ashaft, wherein a demand at the shaft is variable within a lower limitand an upper limit, wherein the oracle circuit is further configured tocompute the MINLP non-generator feasibility based at least in part onthe upper limit, and wherein the oracle circuit is further configured tocompute the MINLP generator feasibility based at least in part on thelower limit.
 7. The system of claim 3, wherein the plurality of processunits within the continuous process includes a stream, wherein a sourcesupplying the stream is variable within a lower limit and an upperlimit, wherein the oracle circuit is further configured to compute thenon-MINLP feasibility based at least in part on a load at a sink of thestream, wherein the oracle circuit is further configured to compute theMINLP non-generator feasibility based at least in part on the upperlimit, and wherein the oracle circuit is further configured to computethe MINLP generator feasibility based at least in part on the lowerlimit.
 8. The system of claim 1, wherein the oracle circuit is furtherconfigured to generate and maintain a list of infeasible switchingstates, and wherein the infeasibility indication is based at least inpart on the list.
 9. The system of claim 1, wherein the oracle circuitis further configured to group a plurality of model circuits into agroup, wherein each model circuit of the group does not contradict anyother model circuit of the group, and wherein the infeasibilityindication is based at least in part on the group.
 10. The system ofclaim 1, wherein the oracle circuit is further configured to determinewhether a cost of the specified switching state is greater than a costof the current state, wherein the infeasibility indication is based atleast in part on the determination.
 11. A computer-implemented methodfor generating an optimal operating state of a continuous process, themethod comprising: receiving, by a control system, data from at leastone sensor within the continuous process, the data representing acurrent state of each of a plurality of process units within thecontinuous process, the process units meeting one or more demands of thecontinuous process; simulating, by the control system, an operation of aplurality of unit models in conjunction with a mixed integer nonlinearprogramming (MINLP) solver in real-time, the plurality of unit modelseach representing one of the plurality of process units via at least onefirst-principle equation, the plurality of unit models each having anMINLP switch implementing MINLP behavior of the unit model, and eachMINLP switch encoding at least one operating constraint of thecontinuous process; and generating, by the control system, aninfeasibility indication as a function of the demands, the infeasibilityindication indicating whether a switching state of a plurality ofswitching states each corresponding to an operational status of theplurality of unit models is infeasible.
 12. The method of claim 11,further comprising generating, by the control system, an operating stateof the continuous process based at least in part on the infeasibilityindication, wherein the operating state is optimized in accordance withthe at least one operating constraint of the continuous process.
 13. Themethod of claim 11, further comprising: generating, by the controlsystem, a non-MINLP feasibility of one or more non-MINLP process unitsof the plurality of process units; generating, by the control system, aMINLP non-generator feasibility of one or more MINLP non-generatorprocess units of the plurality of process units and the non-MINLPfeasibility; and generating, by the control system, a MINLP generatorfeasibility of one or more MINLP generator process units of theplurality of process units and the MINLP non-generator feasibility,wherein the infeasibility indication is based on the non-MINLPfeasibility, the MINLP non-generator feasibility, and the MINLPgenerator feasibility.
 14. The method of claim 13, further comprising:generating, by the control system, the infeasibility indication when thenon-MINLP feasibility is greater than zero; generating, by the controlsystem, the infeasibility indication when the MINLP non-generatorfeasibility is less than zero; and generating, by the control system,the infeasibility indication when the MINLP generator feasibility is oneof zero and greater than zero.
 15. The method of claim 13, wherein theplurality of process units within the continuous process include ashaft, and wherein a demand at the shaft is fixed.
 16. The method ofclaim 13, wherein the plurality of process units within the continuousprocess include a shaft, and wherein a demand at the shaft is variablewithin a lower limit and an upper limit, and the method furthercomprising: generating, by the control system, the MINLP non-generatorfeasibility based at least in part on the upper limit; and generating,by the control system, the MINLP generator feasibility based at least inpart on the lower limit.
 17. The method of claim 11, further comprisinggenerating and maintaining, by the control system, a list of infeasibleswitching states, wherein the infeasibility indication is based at leastin part on the list.
 18. The method of claim 11, further comprisinggrouping, by the control system, one or more of the plurality of unitmodels into a group, wherein each unit model of the group does notcontradict any other unit model of the group, and wherein theinfeasibility indication is based at least in part on the group.
 19. Themethod of claim 11, further comprising determining, by the controlsystem, whether a cost of the switching state is greater than a cost ofthe current state, wherein the infeasibility indication is based atleast in part on the determination.
 20. A computer-readable storagedevice having computer-executable modules stored thereon, that whenexecuted by a processor, generate an operating state of a continuousprocess, said modules comprising: a plurality of model modules eachdefining a plurality of unit models, each unit model representing aprocess unit within the continuous process via at least onefirst-principle equation during an execution of the model module by theprocessor, the process unit meeting at least one demand of thecontinuous process; a plurality of mixed integer nonlinear programming(MINLP) switch modules each transitioning a corresponding model modulebetween an active state and an inactive state based at least in part ona parameter encoding at least one operating constraint of the continuousprocess during an execution of the MINLP switch module by the processor,the plurality of MINLP switch modules each implementing an MINLPbehavior of the corresponding model module; and a solver modulesimulating an operation of each of the model modules and the MINLPswitch modules in real-time during an execution of the solver module bythe processor to generate the operating state of the continuous processbased on a state of the plurality of MINLP switch modules when thesolver module determines the state of the plurality of MINLP switchmodules is feasible as a function of the demand.